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Mathematical game theory, a branch of economics, views any multi-agent environment as a game provided that the impact of each agent on the others is “significant,” regardless of whether the agents are cooperative or competitive.
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Zero sum games are the one in which there are two agents whose actions must alternate and in which the utility values at the end of the game are always the same.
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The minimax algorithm computes the minimax decision from the current state. It uses a simple recursive computation of the minimax values of each successor state, directly implementing the defining equations. The recursion proceeds all the way down to the leaves of the tree, and then the minimax values are backed up through the tree as the recursion unwinds.